Interactive physics simulator
First Law of Thermodynamics
Explore the conservation of energy in thermodynamic systems. Observe how heat input, mechanical work, and molecular internal energy balance inside a piston-cylinder heat engine in real time.
Piston Cylinder Heat Engine Lab
Select a thermodynamic preset or manually modify the heat rate and load weights. Observe energy conservation in the bottom formula.
Live Telemetry
- Heat added (Q)
- 0.0 J
- Change in Int. Energy (ΔU)
- 0.0 J
- Work Done by Gas (W)
- 0.0 J
- Gas Pressure (P)
- 101.3 kPa
- Gas Volume (V)
- 4.0 L
- Gas Temp (T)
- 300.0 K
- First Law Equation (Q = ΔU + W)
- 0.0 J = 0.0 J + 0.0 J
What is the First Law of Thermodynamics?
The First Law of Thermodynamics is a fundamental law of physics stating that energy cannot be created or destroyed, only transformed from one form to another. In thermodynamic systems, it describes how heat transfer, work done, and internal energy are related.
When heat is absorbed by a system, it can raise the internal energy of the system (manifested as an increase in temperature) and/or enable the system to perform mechanical work on its surroundings.
Mathematically, the first law is expressed as:
Where:
- Q is the net heat energy added to the system (in Joules, J).
- ΔU is the change in internal energy of the system (in Joules, J).
- W is the work done BY the system on its surroundings (in Joules, J).
Alternatively, it is often written as ΔU = Q − W, highlighting that the change in internal molecular energy is the heat absorbed minus the energy expended doing work on the environment.
Conservation of Energy
The First Law is simply the Law of Conservation of Energy applied to heat and thermal systems. Any heat energy added to the cylinder must either go into speeding up the gas molecules (increasing temperature and internal energy ΔU) or expanding the chamber against external forces (performing mechanical work W).
Sign Conventions
Sign conventions are critical for avoiding errors when applying the First Law:
- Q > 0: Heat is absorbed by the gas (heating).
- Q < 0: Heat is released by the gas (cooling).
- W > 0: Gas expands, doing work ON the piston.
- W < 0: Piston compresses the gas (work done ON the gas).
- ΔU > 0: Temperature of the gas increases.
- ΔU < 0: Temperature of the gas decreases.
Solved Examples
A thermodynamic system undergoes a process in which it absorbs 800 J of heat from its surroundings. At the same time, the gas expands and does 300 J of work on the surroundings. Find the change in the internal energy of the system.
- Identify the given values and apply sign conventions:
- Heat absorbed by the system (Q) = +800 J (positive because heat enters the system).
- Work done by the system (W) = +300 J (positive because the system does work on the surroundings).
- Write down the First Law of Thermodynamics equation: Q = ΔU + W.
- Rearrange the equation to solve for the change in internal energy (ΔU): ΔU = Q − W.
- Substitute the values: ΔU = 800 J − 300 J = 500 J.
- Since ΔU is positive, the internal energy of the system increases by 500 Joules.
Answer: +500 J (Internal energy increased by 500 J)
During a compression process, 400 J of work is done ON a gas contained in a cylinder. If the cylinder is wrapped in a thick insulation jacket (making it adiabatic), determine the heat transfer Q and find the change in the internal energy of the gas.
- Identify the process type: Since the cylinder is adiabatic (insulated), no heat enters or leaves. Therefore, heat transfer Q = 0 J.
- Identify the work term and its sign: Work is done ON the gas. In our physics convention (where W is work done BY the gas), work done ON the gas is negative: W = −400 J.
- Write down the First Law equation: Q = ΔU + W.
- Substitute Q and W into the equation: 0 = ΔU + (−400 J).
- Solve for ΔU: ΔU = +400 J.
- This shows that the work done to compress the gas is converted entirely into internal energy, raising the temperature of the gas.
Answer: Q = 0 J (Adiabatic), ΔU = +400 J (Temperature rises)
A gas undergoes an isothermal expansion in which it does 600 J of work. Calculate the amount of heat absorbed by the gas during this process.
- Identify the process type: The process is isothermal (constant temperature).
- Since the temperature is constant, the average kinetic energy of the ideal gas molecules does not change, meaning the change in internal energy is zero: ΔU = 0 J.
- Write down the First Law equation: Q = ΔU + W.
- Substitute ΔU = 0 J into the equation: Q = 0 + W.
- Since work done by the gas (W) is +600 J (expansion), the heat absorbed is: Q = +600 J.
- Therefore, all the heat energy absorbed is converted directly into work done by the expanding gas, keeping the internal temperature constant.
Answer: +600 J of heat absorbed
Common Mistakes
- Confusing the sign of Work W: Be careful whether work is done by the gas or on the gas. Work done on the gas decreases the volume (ΔV is negative) and contributes negatively to the Q = ΔU + W formula.
- Assuming no heat transfer during isothermal processes: Because temperature remains constant (ΔU = 0), students often assume heat transfer Q = 0. However, in an isothermal expansion, heat must enter the gas slowly to compensate for the expansion cooling, ensuring Q = W.
- Assuming adiabatic means constant temperature: Adiabatic simply means no heat transfer (Q = 0). When a gas is compressed adiabatically, the work done on it increases its internal energy, causing its temperature to rise significantly.
Thermodynamic Processes Summary
The First Law simplifies uniquely for the four standard thermodynamic paths:
- Isobaric (Const. P): Pressure remains constant. Work is done, and heat changes both U and volume: Q = ΔU + PΔV.
- Isochoric (Const. V): Volume remains constant, meaning no work is done: W = 0, so Q = ΔU.
- Isothermal (Const. T): Temperature is constant, meaning internal energy doesn't change: ΔU = 0, so Q = W.
- Adiabatic (Q = 0): No heat enters or leaves the system: Q = 0, so ΔU = −W.
Practice Questions
1. A gas is heated at constant volume (isochoric process) and absorbs 150 J of heat. How much work is done by the gas, and what is the change in its internal energy?
Since the volume is held constant, there is no displacement of the boundary (displacement dx = 0). Consequently, the work done is zero (W = PΔV = 0 J). Applying the First Law (Q = ΔU + W), we get 150 J = ΔU + 0. Thus, the change in internal energy is ΔU = +150 J. All the heat absorbed goes entirely into increasing the system's temperature.
2. What is the physical meaning of the First Law of Thermodynamics, and what fundamental law of physics is it based on?
The First Law of Thermodynamics is a statement of the Law of Conservation of Energy adapted for thermodynamic systems. It states that energy cannot be created or destroyed, only converted from one form to another. Specifically, the total energy entering a system as heat must equal the increase in the system's internal molecular energy plus the mechanical work done by the system.
3. Explain why the temperature of a gas drops when it undergoes rapid adiabatic expansion (like when releasing air from a pressurized tire).
In an adiabatic expansion, the system does work on the surroundings (W is positive) but receives no heat input (Q = 0). According to the First Law, Q = ΔU + W, which becomes 0 = ΔU + W, or ΔU = −W. Because work is positive, ΔU must be negative. The system draws energy from its own internal energy to do the expansion work, causing the molecular kinetic energy (and thus the temperature) of the gas to drop.
4. Under what condition does the work done by a gas equal the negative of its change in internal energy?
This condition occurs in an adiabatic process (where heat transfer Q = 0). Substituting Q = 0 into the First Law (Q = ΔU + W) yields 0 = ΔU + W, which simplifies to W = −ΔU or ΔU = −W. In this case, work is done solely at the expense of internal energy.
FAQ
Frequently Asked Questions
What is the First Law of Thermodynamics?
The First Law of Thermodynamics states that the net heat added to a system is equal to the change in the internal energy of the system plus the work done by the system on its surroundings. Mathematically: Q = ΔU + W.
What does the symbol ΔU represent?
ΔU represents the change in the internal energy of the system. Internal energy is the sum of the kinetic and potential energies of all the microscopic particles (atoms and molecules) that make up the system.
What are the sign conventions for heat (Q)?
Heat (Q) is positive (+) if heat is absorbed by the system (added to it). Heat (Q) is negative (−) if heat is released by the system (removed from it).
What are the sign conventions for work (W)?
Work (W) is positive (+) if work is done BY the system (expansion). Work (W) is negative (−) if work is done ON the system (compression). Note: Some chemistry textbooks write the law as ΔU = Q + W, where W is work done ON the system. Both represent the same physical conservation of energy.
Is the First Law of Thermodynamics ever violated?
No. To date, no physical process in the universe has been shown to violate the conservation of energy. It is a fundamental law of physics.
What is an isobaric process?
An isobaric process is a thermodynamic process that occurs at constant pressure. The work done by the gas during this process is W = P · ΔV.
What is an isochoric process?
An isochoric (or isovolumetric) process occurs at constant volume. Because the volume cannot change, the gas does no mechanical work (W = 0), and any heat transfer changes the internal energy directly (Q = ΔU).
What is an isothermal process?
An isothermal process occurs at constant temperature. For an ideal gas, since temperature does not change, the change in internal energy is zero (ΔU = 0), meaning all heat added is converted into work (Q = W).
What is an adiabatic process?
An adiabatic process occurs with zero heat exchange between the system and its surroundings (Q = 0). This is achieved by either perfectly insulating the system or conducting the process so rapidly that heat has no time to flow.
How does a refrigerator utilize the First Law?
A refrigerator does mechanical work (using a compressor) on a refrigerant gas to pump heat out of the cold interior and expel it into the warmer room. The First Law describes this balance of electrical work input, heat extracted, and heat exhausted.
What is a heat engine?
A heat engine is a device that converts thermal energy (heat) into mechanical energy (work) in a cyclic process. It absorbs heat from a hot reservoir, performs work, and expels the remaining waste heat to a cold reservoir.
Can a system convert heat entirely into work in a cycle?
No. While an isothermal process can convert heat entirely into work during a single expansion, the Second Law of Thermodynamics states that it is impossible for a cyclic heat engine to convert all absorbed heat entirely into work without expelling waste heat.